Voters want Britain to scrap nuclear weapons altogether rather than replace Trident, according to a new Guardian/ICM poll today. The result marks a sharp turnaround in public opinion amid growing debate about the cost of a new generation of nuclear weapons and the impact of conventional defence cutbacks on the war in Afghanistan.

For decades nuclear disarmament has been seen as a minority issue, with most voters assumed to favour continued investment in an independent British nuclear weapons system. But today's poll shows that 54% of all voters would prefer to abandon nuclear weapons rather than put money into a new generation of Trident warheads, as the government plans.

Last week's G8 summit brought suggestions that Britain might include Trident in international disarmament talks. "What we need is collective action by the nuclear weapons powers to say that we are prepared to reduce our nuclear weapons," said Gordon Brown.

Today's figures mark a dramatic turnaround in public opinion since Trident renewal was announced by Brown three years ago. In July 2006, 51% backed renewal, while 39% opposed it. Since then support for a new Trident system has fallen by nine points while opposition has grown by 15 points.

Overall, only 42% of all voters now back renewal, according to the poll. Until now a majority of voters have always supported a British nuclear system, although one other recent ICM poll showed most people wanting to extend the life of the existing Trident system rather than spend money upgrading it.

In 2006 Gordon Brown reaffirmed Britain's commitment to Trident, and the government won Commons backing, thanks to Tory support. A design contract is expected to be signed this September, during the parliamentary recess, and the nuclear weapons were excluded from the defence review announced last week.

The poll shows for the first time that a majority of Labour voters oppose nuclear weapons, as well as most Liberal Democrats.

On balance, 59% of Labour voters want Britain to scrap nuclear weapons, against 40% who want to replace them. In 2006 Trident renewal was backed by a majority of Labour voters. Even among Conservative voters, 41% would now rather see unilateral nuclear disarmament than a new generation of weapons. That may encourage the opposition to defer renewal as part of a package of spending cuts.

Today's results are one consequence of the growing political battle over public spending, with retired defence chiefs, Labour and Liberal Democrat MPs suggesting that the £20bn cost of replacing Trident would be better spent on conventional forces.

The poll also suggests that the Conservatives are outflanking Labour in the debate over spending. More than two-thirds of voters say they want spending to be cut, double the proportion who believe the government should increase expenditure, as some ministers continue to argue. Even a majority of Labour voters want to see cutbacks.

As a result the Conservative party has extended its lead over Labour to 14 points. At 41%, up two, Tory support is at its highest in an ICM poll since March, before the expenses scandal broke. Labour, unchanged on 27%, is stuck on its second-lowest ICM score since June last year.

The Liberal Democrats are on 20%, up two points, while backing for other parties is 12%, down three as minor party support from the European elections fades.

• ICM Research interviewed a random sample of 1,000 adults aged 18+ by telephone on 10-11 July 2009. ICM is a member of the British Polling Council and abides by its rules.